{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ELBN2KRC5JLKSS5U4NAZDZWRLS","short_pith_number":"pith:ELBN2KRC","schema_version":"1.0","canonical_sha256":"22c2dd2a22ea56a94bb4e34191e6d15ca8a2a438d49d4d57dd5317fd09793fce","source":{"kind":"arxiv","id":"2206.08805","version":1},"attestation_state":"computed","paper":{"title":"Complexity of the Multiobjective Spanner Problem","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.CC","authors_text":"Fritz B\\\"okler, Henning Jasper","submitted_at":"2022-06-17T14:35:40Z","abstract_excerpt":"In this paper, we take an in-depth look at the complexity of a hitherto unexplored Multiobjective Spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied Minimum t-Spanner problem. This multiobjective approach allows us to find solutions that offer a viable compromise between cost and utility. Thus, the MSp can be a powerful modeling tool when it comes to the planning of, e.g., infrastructure. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is BUCO-hard. Additionally, we prove that if P != NP, neit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2206.08805","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2022-06-17T14:35:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"b90ec264e16ec1e3bcbcd792b9366224c816647ad8c80bb54f2e17b5bf7c4f0a","abstract_canon_sha256":"ed69ac3c439d4be1c9a26c014d20ca1d4a3e32760ef70678519a3bb7ae8bbf97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:43.542185Z","signature_b64":"PIKDTG+LNYmwMoi7MLk3Ztp3RjEJ0LFkOxMNl43RAHJzUYNZ3GRqyV/YsrdDpc33paSd5o6EOC54SZs5oWCzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22c2dd2a22ea56a94bb4e34191e6d15ca8a2a438d49d4d57dd5317fd09793fce","last_reissued_at":"2026-07-05T04:32:43.541784Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:43.541784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complexity of the Multiobjective Spanner Problem","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.CC","authors_text":"Fritz B\\\"okler, Henning Jasper","submitted_at":"2022-06-17T14:35:40Z","abstract_excerpt":"In this paper, we take an in-depth look at the complexity of a hitherto unexplored Multiobjective Spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied Minimum t-Spanner problem. This multiobjective approach allows us to find solutions that offer a viable compromise between cost and utility. Thus, the MSp can be a powerful modeling tool when it comes to the planning of, e.g., infrastructure. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is BUCO-hard. Additionally, we prove that if P != NP, neit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08805","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.08805/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2206.08805","created_at":"2026-07-05T04:32:43.541848+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.08805v1","created_at":"2026-07-05T04:32:43.541848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08805","created_at":"2026-07-05T04:32:43.541848+00:00"},{"alias_kind":"pith_short_12","alias_value":"ELBN2KRC5JLK","created_at":"2026-07-05T04:32:43.541848+00:00"},{"alias_kind":"pith_short_16","alias_value":"ELBN2KRC5JLKSS5U","created_at":"2026-07-05T04:32:43.541848+00:00"},{"alias_kind":"pith_short_8","alias_value":"ELBN2KRC","created_at":"2026-07-05T04:32:43.541848+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS","json":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS.json","graph_json":"https://pith.science/api/pith-number/ELBN2KRC5JLKSS5U4NAZDZWRLS/graph.json","events_json":"https://pith.science/api/pith-number/ELBN2KRC5JLKSS5U4NAZDZWRLS/events.json","paper":"https://pith.science/paper/ELBN2KRC"},"agent_actions":{"view_html":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS","download_json":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS.json","view_paper":"https://pith.science/paper/ELBN2KRC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.08805&json=true","fetch_graph":"https://pith.science/api/pith-number/ELBN2KRC5JLKSS5U4NAZDZWRLS/graph.json","fetch_events":"https://pith.science/api/pith-number/ELBN2KRC5JLKSS5U4NAZDZWRLS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/action/storage_attestation","attest_author":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/action/author_attestation","sign_citation":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/action/citation_signature","submit_replication":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/action/replication_record"}},"created_at":"2026-07-05T04:32:43.541848+00:00","updated_at":"2026-07-05T04:32:43.541848+00:00"}